ABC SMC is a Bayesian parameter inference algorithm which is based on efficient simulation of mechanistic models. We have adapted it for model selection by defining it on an extended parameter space (M, \theta). Model selection ABC SMC algorithm chooses the best model for the system given the set of available models, balancing the fit to the data and the complexity of the model. , Here we apply it to the phosporylation dynamics of Erk MAP kinase. It has been demonstrated that in vitro phosphorylation and dephosphorylation of MAPK occur though a distributive mechanism (Burack 1997, Ferrell 1997, Zhao 2001). Recently, novel experimental techniques based on automated high-throughput immunostaining and image processing have allowed for collection of data based on population of individual cells in vivo (Ozaki et al., in preparation). We are going to examine four different hypotheses , 1) distributive phosphorylation and dephosphorylation , 2) processive phosphorylation and dephosphorylation , 3) distributive phosphorylation, processive dephosphorylation , 4) processive phosphorylation, distributive dephosphorylation , modeled by kinetic ODE models and employ Bayesian model selection tool based on ABC SMC algorithm (Toni et al., 2009) to determine the most likely mechanisms of phosphorylation and dephosphorylation occuring in Erk signaling pathway in vivo.